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Artículo
Asymptotic behavior of nonlinear elliptic systems on varying domains
(Society for Industrial and Applied Mathematics, 2000)
We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, ...
Artículo
Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design
(Elsevier, 2006-07-15)
In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients and the domains vary arbitrarily. Here, we improve the convergence result given in this paper ...
Artículo
Nonlocal limits in the study of linear elliptic systems arising in periodic homogenization
(Elsevier, 2007-07-01)
In the present paper, we obtain the two-scale limit system of a sequence of linear elliptic periodic problems with varying coefficients. We show that this system has not the same structure than the classical one, obtained ...
Artículo
Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
(Elsevier, 2008-10-15)
This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using ...
Artículo
The limit of Dirichlet systems for variable monotone operators in general perforated domains
(Elsevier, 2001-11-15)
We study the asymptotic behaviour of the solutions of nonlinear Dirichlet systems when the operators and the open sets where they are posed vary simultaneously. We obtain a representation of the limit problem and we prove ...
Artículo
The two-scale convergence method applied to generalized Besicovitch spaces
(The Royal Society, 2002-12-08)
The two-scale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems. In the present paper we develop this theory to generalized Besicovitch spaces, which include the ...
Artículo
The div-curl lemma “trente ans après”: an extension and an application to the G-convergence of unbounded monotone operators
(Elsevier, 2009-05)
In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn where the sequences vn and wn are respectively bounded in Lp(Ω)N and Lq(Ω)N, while divvn and curlwn are ...
Artículo
Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
(EDP Sciences, 2009)
For a fixed bounded open set Ω ⊂ RN , a sequence of open sets Ωn ⊂ Ω and a sequence of sets Γn ⊂ ∂Ω ∩ ∂Ωn, we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ωn, satisfying Neumann ...
Artículo
Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization
(Taylor & Francis, 2007-06-06)
In this paper, we study the asymptotic behaviour of sequences of conduction problems and sequences of the associated diffusion energies. We prove that, contrary to the three-dimensional case, the boundedness of the ...
Artículo
Asymptotic behaviour of linear Dirichlet parabolic problems with variable operators depending on time in varying domains
(Elsevier, 2005-06-01)
We study the asymptotic behaviour of the solutions of linear parabolic Dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously. In the limit problem it appear the H-limit ...